Frequency Analysis of TWX

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From the Update 11/5/2010: The strongest frequency, according to classical frequency analysis, is an oscillation with a length of 8 trading sessions.

Frequency Analysis based on Monthly Comb

Frequency Analysis based on Monthly Comb of AOL Time Warner

Even a casual examination of historical price lines seems to reveal cycles or regular short term fluctuations that continue repeating. Through the years, technicians have expended much effort to measure and exploit these cycles. It would appear simple enough to do a frequency analysis on the time series. But the cycles or periods that seem so easy to see in the price data, have proven to be surprisingly difficult to measure by classical methods. The classical methods apply to stationary cycles of exactly regular period. We can easily remove the trends from historical price data to make the series stationary. However, the fluctuations seen in financial data are almost never exactly periodic, complicating most attempts to take advantage of these cycles.

One factor in the behaviour of market fluctuations is "Anticipation". When speculators detect a cycle in prices, they will buy earlier before the peak, and sell earlier before the dip. This phenomena causes an increase in frequency, and eventually a breakup of the established cycle. Traditional frequency analysis methods such as the Fourier Transform, break down badly attempting to deal with these irregularities.

Wilder estimated that there was an important period of about 28 trading sessions. The half cycle of this period (14 sessions) is a default factor in many of the technical indicators. We have found this to be a reasonable figure, even in today's markets, but there is significant variation between issues. Some companies just seem to have faster or slower cycles for one reason or another, and the indicators may be more accurate when fitted to the situation.

The paradoxical condition of variable length periods forces the adoptation of some new forms of analysis.




General Market Conditions

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More than 70 Hi-Rez charts daily for AOL Time Warner:

Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 29.00
Sawtooth = 50.49
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High16.7329.0029.0022.99 %
Low18.3031.0025.0017.43 %
Recent HighPriceRecent LowPrice Cycle
Monday, October 04, 201030.1624
Monday, September 20, 201031.9131
Monday, August 30, 201029.5740
Thursday, August 05, 201032.6634
Friday, July 02, 201028.0030
Thursday, June 17, 201032.8032
Thursday, May 20, 201029.3278
Monday, May 03, 201033.40112


Fourier Transform after Digital Filter M

Cycle LengthFourier Amplitude
80.81
130.59
160.42
180.37
220.32
200.31
250.29
300.23
330.22
420.14
370.14



Frequency Analysis based on Quarterly Comb

Frequency Analysis based on Quarterly Comb of AOL Time Warner

Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 67.00
Sawtooth = 52.82
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High45.8981.0067.0027.99 %
Low53.2291.0067.0021.63 %
Recent HighPriceRecent LowPrice Cycle
Thursday, August 05, 201032.6634
Friday, July 02, 201028.00108
Thursday, June 17, 201032.8032
Thursday, January 28, 201026.23227
Monday, May 03, 201033.40112
Thursday, March 05, 200915.0070
Wednesday, November 18, 200931.92220
Thursday, November 20, 200814.7893


Fourier Transform after Digital Filter Q

Cycle LengthFourier Amplitude
80.46
130.27
250.19
200.18
220.17
1780.15
1240.14
950.14
320.13
6830.12
1410.12



Frequency Analysis based on Yearly Comb

TWX:  Frequency Analysis based on Yearly Comb

Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 60.65
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High0.000.000.000.00 %
Low0.000.000.000.00 %
Recent HighPriceRecent LowPrice Cycle
Monday, May 03, 201033.40419
Thursday, November 20, 200814.78593
Tuesday, September 02, 200834.91409
Monday, July 17, 200631.99258
Thursday, January 18, 200746.86335
Thursday, July 07, 200532.59227
Friday, September 16, 200538.01182
Thursday, August 12, 200431.29370


Fourier Transform on Raw Closing Prices

Cycle LengthFourier Amplitude
67.84
6836.36
8196.23
5124.92
134.51
4554.16
1783.84
1953.11
1862.96
5852.83
2412.65




Breaking News:

Monday, November 15, 2010: We have news on PG&E Corporation, ticker symbol PCG. A significant moving average event has happened. Also, there are breaking events concerning Cree, Inc. and Abbott Laboratories.

From the News Archive: (11/12/2010 ) A favorable event happened at PetSmart, Inc. Meanwhile, bad news came from Intel, Chesapeake Energy Corporation, and JP Morgan Chase.



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TWX




AOL Time Warner












Average Sawtooth based on Monthly Combo

TWX:  Average Sawtooth based on Monthly Combo

TWX




AOL Time Warner









Average Sawtooth based on Bi-weekly Combo

Average Sawtooth based on Bi-weeklyly Combo of AOL Time Warner



Comparing the length of time from high points to successive lowpoints, against the corresponding time span from the lows to the following periodic highs, gives us the Sawtooth Indicator. The mid-point, corresponding to a perfect sine wave, is 50 percent. Values less than this indicate the sell slope is steeper than the buy slope, while values over 50 percent show the opposite.

This is supposed to indicate the degree of fear or greed. The chart represents the sawtooth percentage of (approximately) monthly cycles over the past year, and of the (approximately) bi-weekly cycles, averaged over the past six months.

.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25Signaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 0 instances
Sell Signals - 0 instances
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals middle CrossingSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 14 instances
Future30SesAvgClose 2.10 % minus 3.74 % = -1.65 %-13.94 %
Future5SesAvgClose 0.70 % minus 0.73 % = -0.03 %-1.58 %
Future2SesAvgClose 0.53 % minus 0.37 % = 0.17 %20.96 %
Sell Signals - 13 instances
Future30SesAvgClose 5.06 % minus 3.74 % = 1.32 %11.17 %
Future5SesAvgClose 1.35 % minus 0.73 % = 0.62 %31.51 %
Future2SesAvgClose 1.26 % minus 0.37 % = 0.90 %113.86 %
.
Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30Signaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 2 instances
Future30SesAvgClose 2.20 % minus 3.74 % = -1.54 %-13.07 %
Future5SesAvgClose 7.24 % minus 0.73 % = 6.51 %330.67 %
Future2SesAvgClose 4.18 % minus 0.37 % = 3.81 %483.74 %
Sell Signals - 4 instances
Future30SesAvgClose 0.20 % minus 3.74 % = -3.55 %-30.03 %
Future5SesAvgClose 2.70 % minus 0.73 % = 1.97 %99.95 %
Future2SesAvgClose 2.70 % minus 0.37 % = 2.34 %296.76 %
.
Projection of Representative Monthly CycleSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 83 instances
Future30SesAvgClose 4.07 % minus 3.74 % = 0.33 %2.77 %
Future5SesAvgClose 1.33 % minus 0.73 % = 0.60 %30.43 %
Future2SesAvgClose 0.74 % minus 0.37 % = 0.37 %47.62 %
Sell Signals - 90 instances
Future30SesAvgClose 3.16 % minus 3.74 % = -0.59 %-4.97 %
Future5SesAvgClose -0.38 % minus 0.73 % = -1.11 %-56.26 %
Future2SesAvgClose -0.48 % minus 0.37 % = -0.85 %-107.73 %
.
Projection of BiWeekly Modal CyclesSignaled Appreciation minus non-signaled AppreciationAnnualized %
Buy Signals - 175 instances
Future30SesAvgClose 4.03 % minus 3.74 % = 0.29 %2.42 %
Future5SesAvgClose 0.92 % minus 0.73 % = 0.19 %9.42 %
Future2SesAvgClose 0.43 % minus 0.37 % = 0.07 %8.31 %
Sell Signals - 165 instances
Future30SesAvgClose 3.70 % minus 3.74 % = -0.04 %-0.37 %
Future5SesAvgClose 1.05 % minus 0.73 % = 0.32 %16.27 %
Future2SesAvgClose 0.66 % minus 0.37 % = 0.30 %37.60 %
.
The best buy signal for 30 future sessions was 0.33 % from the Projection of Representative Monthly Cycle,and the best sell signal for was -3.74 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 75 and 25.
For 5 future sessions the best buy signal was 6.51 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal was -1.11 % from the Projection of Representative Monthly Cycle.
The best buy signal for 2 future sessions was 3.81 % from the Semi-Annual Avg. of Bi-weekly Sawtooth Signals at 70 and 30,and the best sell signal was -0.85 % from the Projection of Representative Monthly Cycle.



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